where, \(\psi _\ell \) , \( \xi _\ell \)  are Riccati-Bessel functions [1]}, \(m = n /n_1\)  is the relative refractive index.
In order to study the directional scattering pattern, the expressions for differential scattering efficiencies in forward (\(\theta =0\) ) and
backward (\(\theta = \pi )\)  directions are given as [2]}
\(Q_b|_{\theta =\pi }= \frac{1}{x^2}\bigg | { \sum _{\ell =1}^\infty }{(2\ell +1)(-1)^l(a_\ell - b_\ell )} \bigg |^2, \) 
\(Q_f|_{\theta =0}= \frac{1}{x^2}\bigg | { \sum _{\ell =1}^\infty }{(2\ell +1) (a_\ell + b_\ell )} \bigg |^2. \) 
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